Algebraic Topology

Klappentext Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated, and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint. Author C.R.F. Maunder provides examples and exercises; and notes and references at the end of each chapter trace the historical development of the subject. Inhaltsverzeichnis CHAPTER 1 ALGEBRAIC AND TOPOLOGICAL PRELIMINARIES1.1 Introduction 1.2 Set theory1.3 Algebra1.4 Analytic TopologyCHAPTER 2 HOMOTOPY AND SIMPLICIAL COMPLEXES2.1 Introduction 2.2 The classification problem; homotopy2.3 Simplicial complexes2.4 Homotopy and homeomorphism of polyhedra2.5 Subdivision and the Simplicial Approximation Theorem Exercises Notes on Chapter 2CHAPTER 3 THE FUNDAMENTAL GROUP3.1 Introduction 3.2 Definition and elementary properties of the fundamental group3.3 Methods of calculation3.4 Classification of triangulable 2-manifolds Exercises Notes on Chapter 3CHAPTER 4 HOMOLOGY THEORY4.1 Introduction 4.2 Homology groups4.3 Methods of calculation: simplicial homology4.4 Methods of calculation: exact sequences4.5 "Homology groups with arbitrary coefficients, and the Lefschetz Fixed-Point Theorem" Exercises Notes on Chapter 4CHAPTER 5 COHOMOLOGY AND DUALITY THEOREMS5.1 Introduction 5.2 Definitions and calculation theorems5.3 The Alexander-Poincaré Duality Theorem 5.4 Manifolds with boundary and the Lefschetz Duality Theorem Exercises Notes on Chapter 5CHAPTER 6 GENERAL HOMOTOPY THEORY6.1 Introduction 6.2 Some geometric constructions6.3 Homotopy classes of maps6.4 Exact sequences6.5 Fibre and cofibre maps Exercises Notes on Chapter 6CHAPTER 7 HOMOTOPY GROUPS AND CW-COMPLEXES7.1 Introduction 7.2 Homotopy groups7.3 CW-complexes7.4 Homotopy groups of CW-complexes7.5 The theorem of J. H. C. Whitehead and the Cellular Approximation Theorem Exercises Notes on Chapter 7CHAPTER 8 HOMOLOGY AND COHOMOLOGY OF CW-COMPLEXES8.1 Introduction 8.2 The Excision Theorem and cellular homology8.3 The Hurewicz theorem8.4 Cohomology and Eilenberg-MacLane spaces8.5 Products Exercises Notes on Chapter 8ReferencesIndex...

Inhalt
CHAPTER 1 ALGEBRAIC AND TOPOLOGICAL PRELIMINARIES 1.1 Introduction 1.2 Set theory 1.3 Algebra 1.4 Analytic Topology CHAPTER 2 HOMOTOPY AND SIMPLICIAL COMPLEXES 2.1 Introduction 2.2 The classification problem; homotopy 2.3 Simplicial complexes 2.4 Homotopy and homeomorphism of polyhedra 2.5 Subdivision and the Simplicial Approximation Theorem Exercises Notes on Chapter 2 CHAPTER 3 THE FUNDAMENTAL GROUP 3.1 Introduction 3.2 Definition and elementary properties of the fundamental group 3.3 Methods of calculation 3.4 Classification of triangulable 2-manifolds Exercises Notes on Chapter 3 CHAPTER 4 HOMOLOGY THEORY 4.1 Introduction 4.2 Homology groups 4.3 Methods of calculation: simplicial homology 4.4 Methods of calculation: exact sequences 4.5 "Homology groups with arbitrary coefficients, and the Lefschetz Fixed-Point Theorem" Exercises Notes on Chapter 4 CHAPTER 5 COHOMOLOGY AND DUALITY THEOREMS 5.1 Introduction 5.2 Definitions and calculation theorems 5.3 The Alexander-Poincaré Duality Theorem 5.4 Manifolds with boundary and the Lefschetz Duality Theorem Exercises Notes on Chapter 5 CHAPTER 6 GENERAL HOMOTOPY THEORY 6.1 Introduction 6.2 Some geometric constructions 6.3 Homotopy classes of maps 6.4 Exact sequences 6.5 Fibre and cofibre maps Exercises Notes on Chapter 6 CHAPTER 7 HOMOTOPY GROUPS AND CW-COMPLEXES 7.1 Introduction 7.2 Homotopy groups 7.3 CW-complexes 7.4 Homotopy groups of CW-complexes 7.5 The theorem of J. H. C. Whitehead and the Cellular Approximation Theorem Exercises Notes on Chapter 7 CHAPTER 8 HOMOLOGY AND COHOMOLOGY OF CW-COMPLEXES 8.1 Introduction 8.2 The Excision Theorem and cellular homology 8.3 The Hurewicz theorem 8.4 Cohomology and Eilenberg-MacLane spaces 8.5 Products Exercises Notes on Chapter 8 References Index

#	Onlineshop	Preis CHF	Versand CHF	Total CHF
1	Seller	0.00	0.00	0.00